Stochastic inventory routing with dynamic demands and intra-day depletion

Abstract

Businesses such as supermarkets face an inventory routing problem with distinct stochastic dynamic demand distributions for various weekdays and times of the day. Most research, however, considers aggregated per-period demand and inventory depletion, thereby oversimplifying actual events. We formulate the problem as a finite-horizon stochastic dynamic program that accounts for the dynamic demand throughout the planning horizon and within each planning period. The models include different levels of information aggregation to decide the replenishment quantities and times by dividing periods into sub-periods with distinct demand distributions. This division helps the supplier create efficient replenishment plans and account for intra-day inventory levels. The modeled characteristics include routing, holding and stock-out costs, delivery time windows, inventory and vehicle capacities, and delivery time windows. The problem is solved using an iterative lookahead algorithm with an adaptive large neighborhood search for the routing and policy learning for the replenishment decisions. Numerical evaluations show the benefit of intra-day planning, effects of instance sizes, different coefficients of variation, and holding costs compared to benchmark replenishment policies. Considering intra-day depletion and demand data for each sub-period helps achieve savings of more than 20% compared to planning for full periods. The savings are obtained by adjusting delivery quantities, incorporating intra-day consumption, creating more efficient delivery routes, and correctly timing replenishments.